DUMMYA behavioral psychologist is interested in whether goal-setting activities can be applied...

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DUMMYA behavioral psychologist is interested in whether goal-setting activities can be applied successfully in public school classrooms. The psychologist randomly selects 30 middle-schools students and randomly assigns them to three different groups that are assigned different levels of goal difficulty. The dependent variable is performance on a verbal-fluency task. Before the study each student is give a general-ability test, whose scores are used as the covariate. The data for this research scenario are given below. Conduct an analysis of covariance using these data and answer the following questions. Use an alpha = .05 for all statistical tests. The average verbal fluency score is 48.267. The average general ability score is 20.7.  	Group 	Verbal Fluency 	General Ability 	Group 	Verbal Fluency 	General Ability 	1 	42 	16 	2 	50 	20 	1 	40 	16 	2 	62 	23 	1 	48 	19 	2 	60 	24 	1 	55 	24 	2 	48 	21 	1 	45 	20 	2 	47 	20 	1 	51 	22 	3 	46 	20 	1 	47 	20 	3 	47 	21 	1 	38 	23 	3 	43 	19 	1 	46 	20 	3 	54 	26 	1 	45 	18 	3 	49 	21 	2 	51 	25 	3 	44 	25 	2 	50 	18 	3 	53 	24 	2 	45 	17 	3 	52 	23 	2 	52 	19 	3 	42 	18 	2 	47 	17 	3 	49 	22 1. Is the assumption of homogeneity of regression met for these data? What specific information did you use to come to this conclusion? (2 points)  2. Does the covariate, general ability, have a significant relationship to the dependent variable? What specific information did you use to come to this conclusion? (2 points) 3. Assuming that homogeneity of regression was met, are there differences in the mean verbal fluency of the three groups? What specific information did you use to come to this conclusion? (2 points) 4. Assuming you conclude that all three groups are not the same in verbal fluency, use a Bonferroni procedure to determine which of the groups differ. Conduct Cohen’s d standardized mean difference effect sizes for each of these pairwise differences. (4 points) 5. What proportion of variance in verbal fluency can be explained by the general ability and differences among the goal setting groups? What is the strength of association for the goal setting groups for participants that have the same general abilities? (4 points) 6. Write-up the results of your analysis in APA-format including a discussion of assumption testing, results of all statistical analyses, and effect size reporting (6 points).

Suravi · Accepted Answer

1.    Homegeneity of regression means slope of both the variables are similar, they are homogeneous
H0 : There is no homogeneity of regression
H1 : There is homogeneity of regression
	Tests of Between-Subjects Effects
	Dependent Variable:   Verbal_Fluency  
	Source
	Type III Sum of Squares
	df
	Mean Square
	F
	Sig.
	Corrected Model
	416.510a
	5
	83.302
	4.908
	.003
	Intercept
	278.050
	1
	278.050
	16.382
	.000
	Group
	1.353
	2
	.676
	.040
	.961
	General_Ability
	253.610
	1
	253.610
	14.942
	.001
	Group * General_Ability
	5.314
	2
	2.657
	.157
	.856
	Error
	407.356
	24
	16.973
	
	
	Total
	70714.000
	30
	
	
	
	Corrected Total
	823.867
	29
	
	
	
	a. R Squared = .506 (Adjusted R Squared = .403)
From the table above we see sig level for Group*General Ability is 0.856 which is greater than 0.05 so we accept null hypothesis and conclude that the assumption of homogeneity of regression is met.
2.            
              Covariate General ability have significant relationship to the dependent variable verbal fluency with sig value being 0.001
	Tests of Between-Subjects Effects
	Dependent Variable:   Verbal_Fluency  
	Source
	Type III Sum of Squares
	df
	Mean Square
	F
	Sig.
	Corrected Model
	416.510a
	5
	83.302
	4.908
	.003
	Intercept
	278.050
	1
	278.050
	16.382
	.000
	Group
	1.353
	2
	.676
	.040
	.961
	General_Ability
	253.610
	1
	253.610
	14.942
	.001
	Group * General_Ability
	5.314
	2
	2.657
	.157
	.856
	Error
	407.356
	24
	16.973
	
	
	Total
	70714.000
	30
	
	
	
	Corrected Total
	823.867
	29
	
	
	
	a. R Squared = .506 (Adjusted R Squared = .403)
          
3. 
The sig value for group is 0.062 thus there is significant difference in the mean of verbal fluency of the three group  
	Descriptive Statistics
	Dependent Variable:   Verbal_Fluency  
	Group
	Mean
	Std. Deviation
	N
	1.00
	45.7000
	5.03433
	10
	2.00
	51.2000
	5.59365
	10
	3.00
	47.9000
	4.22821
	10
	Total
	48.2667
	5.33003
	30
	ANOVA
	Verbal_Fluency  
	
	Sum of Squares
	df
	Mean Square
	F
	Sig.
	Between Groups
	153.267
	2
	76.633
	3.085
	.062
	Within Groups
	670.600
	27
	24.837
	
	
	Total
	823.867
	29
	
	
	
4. 
	Multiple Comparisons
	Dependent Variable:   Verbal_Fluency  
	Bonferroni  
	(I) Group
	(J) Group
	Mean Difference (I-J)
	Std. Error
	Sig.
	95% Confidence Interval
	
	
	
	
	
	Lower Bound
	Upper Bound
	1.00
	2.00
	-5.50000
	2.22877
	.061
	-11.1888
	.1888
	
	3.00
	-2.20000
	2.22877
	.997
	-7.8888
	3.4888
	2.00
	1.00
	5.50000
	2.22877
	.061
	-.1888
	11.1888
	
	3.00
	3.30000
	2.22877
	.451
	-2.3888
	8.9888
	3.00
	1.00
	2.20000
	2.22877
	.997
	-3.4888
	7.8888
	
	2.00
	-3.30000
	2.22877
	.451
	-8.9888
	2.3888
Below is the Cohen’s d standardized mean difference effect sizes for each of these pairwise differences which was obtained by standardizing Verbal Fluency.
	Multiple Comparisons
	Dependent Variable:   Zscore(Verbal_Fluency)  
	Bonferroni  
	(I) Group
	(J) Group
	Mean Difference (I-J)
	Std. Error
	Sig.
	95% Confidence Interval
	
	
	
	
	
	Lower Bound
	Upper Bound
	1.00
	2.00
	-1.03188957
	.41815320
	.061
	-2.0992084
	.0354292
	
	3.00
	-.41275583
	.41815320
	.997
	-1.4800746
	.6545630
	2.00
	1.00
	1.03188957
	.41815320
	.061
	-.0354292
	2.0992084
	
	3.00
	.61913374
	.41815320
	.451
	-.4481851
	1.6864526
	3.00
	1.00
	.41275583
	.41815320
	.997
	-.6545630
	1.4800746
	
	2.00
	-.61913374
	.41815320
	.451
	-1.6864526
	.4481851
5.
	Tests of Between-Subjects Effects
	Dependent Variable:

A behavioral psychologist is interested in whether goal-setting activities can be applied successfully in public school classrooms. The psychologist randomly selects 30 middle-schools students and...

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